Sample Paper- 2008
Class- X
Subject - Mathematics
General Instructions:
( i ) All questions are compulsory.
( ii ) The question paper consists of 30 questions divided into four sections –A, B, C
and D. Section A contains 10 questions of 1 mark each, Section B is of 5
Questions of 2 marks each, Section C is of 10 questions of 3 marks each and
section D is of 5 questions of 6 marks each.
( iii ) There is no overall choice. However, an internal choice has been provided in
one question of two marks each, three questions of three marks each and two
questions of six marks each.
( iv ) In question on construction, the drawing should be neat and exactly as per
the given measurements.
( v ) Use of calculator is not permitted.
SECTION A
(Questions 1 – 10 carry 1 mark each)
- Given H.C.F ( 306, 657 ) = 9, find L.C.M ( 306, 657 )
- Prove that 3 + 2 √5 is irrational.
- For which value of ‘P’ does the pair of equations has unique solutions.
4x + Py + 8 = 0
2x + 2y + 2 = 0
4. Find the discriminant of the quadratic equation
5. In fig. DE // BC. Find EC.
A
1.5cm 1cm
D E
3cm
B C
6. Find the distance between the points (-5, 7) and (-1, 3).
7. Find the co-ordinates of the centre of a circle whose end points of the diameter are
( 3, -10 ) and ( 1, 4 ).
- If tan 2A = cot ( A – 180 ), where 2A is an acute angle, find the value of A.
- Find the length of the arc of a circle with radius 6cm if the angle of sector is 600.
- One card is drawn from a well shuffled deck of 52 cards. Calculate the probability that the card drawn will be an ace.
SECTION B
(Questions 11 – 15 carry 2 marks each)
11. Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
OR
Show that any positive odd positive integer is of the form 8q + 1, or 8q + 3, 8q + 5, or 8q + 7,
where q is some integer.
- Solve 2x + 3y = 11 and 2x – 4y = - 24 and hence find the value of ‘m’ for
which y = mx + 3.
- Solve:
1 ─ 1 = 3, x ≠ 0, 3
x x – 2
14. Find the 20th term from the last term of the A.P: 3, 8, 13….… 253.
15. If cot θ = 7/8, evaluate (1 + sin θ) (1 – sin θ)
(1 + cos θ)(1 – cos θ)
SECTION C
(Questions16 – 25 carry 3 marks each)
- On dividing x3 – 3x2 + x + 2 by a polynomial g ( x ), the quotient and remainder
where x – 2 and – 2x + 4, respectively. Find g (x).
- Solve the equation graphically x – y + 1 = 0
and 3x + 2y – 12 = 0.
determine the coordinates of the vertices of the triangle formed by these lines
and the x – axis, and shade the triangular region.
- A train travels 360 km at a uniform speed. If the speed had been 5km/hr more, it
would have taken 1 hour less for the same journey. Find the speed of the train.
OR
A motor boat whose speed is 18km/hr in still water takes 1 hour more to go
24km upstream than to return downstream to the same spot. Find the speed of the
stream.
- Find the sum of first 24 terms of the list numbers whose nth term is given by
an = 3 + 2n.
- Show that the points ( 1, 7 ), ( 4, 2 ), ( -1, -1 ) and ( -4, 4 ) are the vertices of a square.
- Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3).
- Prove the following identity:
.
OR
Without using trigonometric tables, evaluate the following:
cotθ.tan( 900- θ ) – sec( 900- θ ).cosecθ + sin2250 + sin2650 + √3( tan50 tan450 tan850 )
- Construct a triangle with sides 5cm, 6cm and 7cm, then another triangle whose sides are
7/5 of the corresponding sides of the first triangle.
- A chord of a circle of radius 15cm subtends an angle of 600 at the centre. Find the area of the corresponding minor and major segments of the circle ( Use π = 3.14 and √3 = 1.73 ).
OR
Find the area of the shaded region in figure, ABCD is a square of side 14 cm.
Q.25 In the following frequency distribution, the frequency of the class –interval
(40-50) is missing. It is known that the mean ofthe distribution is 52.
Find the missing frequency.
Wages / 10-20 / 20-30 / 30-40 / 40-50 / 50-60 / 60-70 / 70-80No of workers / 5 / 3 / 4 / - / 2 / 6 / 13
SECTION D
(Questions 26 – 30 carry 6marks each)
26. In a triangle, if the square of one side is equal to the sum of squares of the remaining
two sides, prove that the angle opposite to the first side is a right angle.
Using the above, do the following:
ABC is an isosceles triangle with AB = BC. If AB2 = 2AC2, prove that ABC is a right
triangle.
- As observed from the top of a 75m high lighthouse from the sea-level, the angles of
depression of two ships are 300 and 450. If one ship is exactly behind the other on the
same side of the light house, find the distance between the two ships.
OR
A tower is surmounted by a flag staff of height h. At a point on the plane, the angle of
elevation of the bottom and top of the flag staff are α and β respectively. Prove that
the height of the tower is h tanα .
tanβ – tanα
- prove that the ratio of the areas of two similar triangles is equal to the ratioof the squares of their corresponding sides.
Use the above theorem, in the following,
If the areas of two similar triangles are equal, prove that they are congruent triangles.
- The radii of the ends of a frustum of a cone 45cm high are 28cm and 7cm. Find its volume
and total surface area.
OR
Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10km/hr. How much
area will it irrigate in 30 minutes, if 8cm standing water is needed?
- The distribution below gives the weights of 30 students of a class. Find the median weight
of the students.
Weight ( in kg ) / 40 - 45 / 45 - 50 / 50 - 55 / 55 - 60 / 60 - 65 / 65 - 70 / 70 - 75Number of students / 2 / 3 / 8 / 6 / 6 / 3 / 2
- A triangle ABC is drawn to circumscribe a circle of radius 4cm such that the segments BD
and DC into which BC is divided by the point of contact D are of lengths 8cm and 6cm
respectively. Find the sides AB and AC.
A
O
C 6cm D 8cm B
MANAVKENDRAGYANMANDIRSCHOOL, KANDARI
GUJARAT -391210
II TERMINAL EXAM, 2007 – 08
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